ON AN EQUATION INVOLVING FRACTIONAL POWERS WITH PRIME NUMBERS OF A SPECIAL TYPE

Abstract

We consider the equation $[p_1^c]+[p_2^c]+[p_3^c]=N$, where $N$ is a sufficiently large integer, and $[t]$ denotes the integer part of $t$. We prove that if $1<c<\frac{17}{16}$, then it has a solution in prime numbers $p_1,p_2,p_3$ such that each of the numbers $p_1+2,p_2+2,p_3+2$ has at most $[\frac{95}{17-16c}]$ prime factors, counted with their multiplicities.